I need to build a soffit

i have an existing finished room where i want to build a soffit. With Ceiling Joists running perpendicular, i have not problem, but where i want to but the soffit on the adjoining wall, there is no ceiling joists to tie into...how do i do that?

i have an existing finished room where i want to build a soffit. With Ceiling Joists running perpendicular, i have not problem, but where i want to but the soffit on the adjoining wall, there is no ceiling joists to tie into...how do i do that?